Engaging Students’ Minds by Bringing Trigonometry to Life! Stephen J. Hegedus Sara Dalton...
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![Page 1: Engaging Students’ Minds by Bringing Trigonometry to Life! Stephen J. Hegedus Sara Dalton shegedus@umassd.edu sdalton@umassd.edu shegedus@umassd.edu sdalton@umassd.edu.](https://reader030.fdocuments.in/reader030/viewer/2022032703/56649d245503460f949faeb3/html5/thumbnails/1.jpg)
Engaging Students’ Minds by Bringing Engaging Students’ Minds by Bringing Trigonometry to Life!Trigonometry to Life!
Stephen J. Hegedus Sara Dalton [email protected] [email protected]
SimCalc Research Projects,Department of Mathematics
University of Massachusetts, Dartmouthmerg.umassd.edu
www.simcalc.umassd.eduDeveloped under NSF-based Grants: REC-0087771, Understanding Classroom Interactions Among Diverse, Connected Classroom Technologies; REC-0337710, Representation, Participation and Teaching in Connected Classrooms; REC-0228515, Scaling Up SimCalc: Professional Development for Leveraging Technology to Teach More Complex Mathematics, Phase I; REC-0437861, Scaling Up Middle School Mathematics Innovations, Phase II
![Page 2: Engaging Students’ Minds by Bringing Trigonometry to Life! Stephen J. Hegedus Sara Dalton shegedus@umassd.edu sdalton@umassd.edu shegedus@umassd.edu sdalton@umassd.edu.](https://reader030.fdocuments.in/reader030/viewer/2022032703/56649d245503460f949faeb3/html5/thumbnails/2.jpg)
SimCalc MathWorldsSimCalc MathWorlds•Dynamic interactive representations that
are linked, e.g. edit a position function and automatically see velocity graphs update
•Graphically and algebraically editable functions
• Import motion data and re-animate (CBR & CBL2)
•Simulations are at the heart of SimCalc - executable representations (Moreno, 2001)
![Page 3: Engaging Students’ Minds by Bringing Trigonometry to Life! Stephen J. Hegedus Sara Dalton shegedus@umassd.edu sdalton@umassd.edu shegedus@umassd.edu sdalton@umassd.edu.](https://reader030.fdocuments.in/reader030/viewer/2022032703/56649d245503460f949faeb3/html5/thumbnails/3.jpg)
![Page 4: Engaging Students’ Minds by Bringing Trigonometry to Life! Stephen J. Hegedus Sara Dalton shegedus@umassd.edu sdalton@umassd.edu shegedus@umassd.edu sdalton@umassd.edu.](https://reader030.fdocuments.in/reader030/viewer/2022032703/56649d245503460f949faeb3/html5/thumbnails/4.jpg)
SimCalc “Connected” SimCalc “Connected” MathWorldsMathWorlds
•New generation of SimCalc that increases participation, motivation and learning
• Exploits wireless networks to allow the aggregation of student work in mathematically meaningful ways
• Teachers have powerful classroom management tools to focus attention and pedagogical agenda
•Student work becomes contextualized into a class of contributions for comparison and generalization
•Mathematical thinking goes from a local to a social activity
![Page 5: Engaging Students’ Minds by Bringing Trigonometry to Life! Stephen J. Hegedus Sara Dalton shegedus@umassd.edu sdalton@umassd.edu shegedus@umassd.edu sdalton@umassd.edu.](https://reader030.fdocuments.in/reader030/viewer/2022032703/56649d245503460f949faeb3/html5/thumbnails/5.jpg)
D B
C
A
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Start at A and go (anti-)clockwise
y=6sin(x-pi/2)+6
y=-6cos(x)+6
![Page 7: Engaging Students’ Minds by Bringing Trigonometry to Life! Stephen J. Hegedus Sara Dalton shegedus@umassd.edu sdalton@umassd.edu shegedus@umassd.edu sdalton@umassd.edu.](https://reader030.fdocuments.in/reader030/viewer/2022032703/56649d245503460f949faeb3/html5/thumbnails/7.jpg)
Start at BAnti-Clockwise:
y=-6cos(x-pi/2)+6y=-6sin(x)+6
Clockwise:y=6sin(x)+6
y=6cos(x-pi/2)+6
![Page 8: Engaging Students’ Minds by Bringing Trigonometry to Life! Stephen J. Hegedus Sara Dalton shegedus@umassd.edu sdalton@umassd.edu shegedus@umassd.edu sdalton@umassd.edu.](https://reader030.fdocuments.in/reader030/viewer/2022032703/56649d245503460f949faeb3/html5/thumbnails/8.jpg)
Start at C and walk (anti)clockwise:
y=6cos(x)+6y=-6sin(x-pi/2)+6
![Page 9: Engaging Students’ Minds by Bringing Trigonometry to Life! Stephen J. Hegedus Sara Dalton shegedus@umassd.edu sdalton@umassd.edu shegedus@umassd.edu sdalton@umassd.edu.](https://reader030.fdocuments.in/reader030/viewer/2022032703/56649d245503460f949faeb3/html5/thumbnails/9.jpg)
Start at D and walkclockwise:
y=-6sin(x)+6y=-6cos(x-pi/2)+6
Start at D and walkanti-clockwise:y=6sin(x)+6
y=6cos(x-pi/2)+6
![Page 10: Engaging Students’ Minds by Bringing Trigonometry to Life! Stephen J. Hegedus Sara Dalton shegedus@umassd.edu sdalton@umassd.edu shegedus@umassd.edu sdalton@umassd.edu.](https://reader030.fdocuments.in/reader030/viewer/2022032703/56649d245503460f949faeb3/html5/thumbnails/10.jpg)
Exploiting Exploiting ConnectivityConnectivity
• Facilitate work-flow,• Aggregate student constructions to: i.
vary essential parameters on a per-student basis, ii. elevate student attention from single objects to parameterized families of objects,
• Provide opportunity for generalization and expose common thought-patterns (e.g. errors)
![Page 11: Engaging Students’ Minds by Bringing Trigonometry to Life! Stephen J. Hegedus Sara Dalton shegedus@umassd.edu sdalton@umassd.edu shegedus@umassd.edu sdalton@umassd.edu.](https://reader030.fdocuments.in/reader030/viewer/2022032703/56649d245503460f949faeb3/html5/thumbnails/11.jpg)
•Students experience and contributions are embedded in a social workspace
•Mathematical structure and understanding can be emergent, e.g. What do you expect to see before I show you the ...
•Representational infrastructure includes data management systems to manage the flow of information and examination of mathematical sub-structures; such power serves a variety of pedagogical needs, and sustains pedagogical flexibility
Some Top-Level Some Top-Level ThoughtsThoughts
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Pedagogical Pedagogical ReflectionsReflections
• Mathematics is about something• With CBR, students think through the mathematics
of change and variation physically, kinesthetically• With SimCalc, we can reanimate, and examine
variation, we can execute the representation dynamically
• With Connectivity, students make personally meaningful mathematical objects to be publicly shared and discussed
• Students math and social experience are deeply intertwined
• Teacher are in a central role to orchestrate whole class of events
![Page 13: Engaging Students’ Minds by Bringing Trigonometry to Life! Stephen J. Hegedus Sara Dalton shegedus@umassd.edu sdalton@umassd.edu shegedus@umassd.edu sdalton@umassd.edu.](https://reader030.fdocuments.in/reader030/viewer/2022032703/56649d245503460f949faeb3/html5/thumbnails/13.jpg)
Engaging Students’ Minds by Bringing Engaging Students’ Minds by Bringing Trigonometry to Life!Trigonometry to Life!
Stephen J. Hegedus Sara Dalton [email protected] [email protected]
SimCalc Research Projects,Department of Mathematics
University of Massachusetts, Dartmouthmerg.umassd.edu
www.simcalc.umassd.eduDeveloped under NSF-based Grants: REC-0087771, Understanding Classroom Interactions Among Diverse, Connected Classroom Technologies; REC-0337710, Representation, Participation and Teaching in Connected Classrooms; REC-0228515, Scaling Up SimCalc: Professional Development for Leveraging Technology to Teach More Complex Mathematics, Phase I; REC-0437861, Scaling Up Middle School Mathematics Innovations, Phase II